On the size dependence of melting parameters for silicon

Using the dependences of melting point T_m and crystallization point T_c on the number of atoms (N) in a spherical silicon crystal that were calculated elsewhere [6] by the method of molecular dynamics, (i) the number of atoms at which the latent heat of the solid–liquid phase transition disappears and (ii) temperature T₀ = T_m(N₀) = _Tc(N₀) below which solidifying nanoclusters remain noncrystalline are estimated. These values are found to be N₀ = 22.8156 and T₀ = 400.851 K. The N dependences for silicon melting parameters, namely, a jump of entropy of melting, latent melting heat, slope of the melting line, and jumps in the surface energy and volume, are derived.     

Bistable surface anchoring and hysteresis of pitch jumps in a planar cholesteric liquid crystal

The relationship between bistable surface anchoring and the pitch jump process is examined for a planar cholesteric liquid crystal. Introducing a high-order, azimuthal surface anchoring potential into a simple model to describe a cholesteric, we derive an expression for the director twist as the natural pitch of the liquid crystal is allowed to vary. Writing the energy in terms of the surface twist, we are able to determine the twists which minimize the total energy of the system. We demonstrate how a pitch jump is related to an energy exchange from one branch of metastable states to another. We then discuss how the co-existence of energy minima and their associated solution branches may help explain the thermal hysteresis observed experimentally in cholesterics in the neighbourhood of a pitch jump. The presence of a higher-order surface energy term can expand the range of anchoring strengths in which pitch jumps are possible. We also investigate the influence of bidirectional surface anchoring on the behaviour of the total energy. Intermediate quarter-turn pitch jumps can occur, depending on the relative strength of the high-order anchoring term, and these can have a significant effect on the system hysteresis.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Effect of the hexagonal warping on the dynamical conductivity of surface states in a topological insulator

We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term,  Π₂ (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.     

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

Electronic and structural transitions in NdFeO<Subscript>3</Subscript> orthoferrite under high pressures

The effect of high pressure up to 65 GPa on the crystal structure and optical absorption spectra of NdFeO₃ orthoferrite single crystals is studied in diamond anvil cells. At P～37.5 GPa, an electronic transition at which the optical absorption edge jumps from ～2.2 to ～0.75 eV is observed. The equation of state V(P) is studied on the basis of the X-ray diffraction data obtained under pressure. This study reveals a first-order structural phase transition at P～37 GPa with a jump of ～4% in the unit cell volume. It is shown that the phase transition observed in rare-earth orthoferrites at 30–40 GPa is a transition of the insulator-to-semiconductor type.     

Analytical model of a Brownian motor with a fluctuating potential

We propose a model of a Brownian motor that performs a useful work against a load force F in an asymmetric periodic potential V(x) = V(x + 2L) that undergoes random shifts by a half period L with a frequency γ. An arbitrarily shaped potential profile is repeated with an energy shift ΔV in both half-periods L, while the periodicity of the function V(x) is ensured by its jumps at x = 0 and x = L. The boundary condition at x = 0 for the distribution function of a Brownian particle allows us to introduce a high and narrow potential barrier V₀ that blocks the reverse current and leads to high efficiency of the motor (the ratio of the useful work done against the load force F to the energy imparted to the particle through the potential shifts). Based on this model, we derived exact analytical expressions for the current J and the efficiency η. In the special case of piecewise-linear potentials, J and η were plotted against F and γ for various values of the parameters ΔV and V₀. We discuss the influence of the potential shape and fluctuation frequency on the main characteristics of the motor.     

The giant volume magnetostriction and colossal magnetoresistance in Eu<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript> manganite

A doped manganite with the composition Eu_0.55Sr_0.45MnO₃ exhibits giant negative magnetostriction and colossal negative magnetoresistance at temperatures in the vicinity of the magnetic phase transformation (T～41 K). In the temperature interval 4.2 K≤T ≤40 K, the isotherms of magnetization, volume magnetostriction, and resistivity exhibit jumps at the critical field strength H_c1, which decreases with increasing temperature. At 70 K ≤T ≤120 K, the jumps on the isotherms are retained, but the shapes of these curves change and the H_c1 value increases with the temperature. At H<H_c1, the magnetoresistance is positive and exhibits a maximum at 41 K; at H>H_c1, the magnetoresistance becomes negative, passes through a minimum near 41 K and then reaches a colossal value. The observed behavior is explained by the existence of three phases in Eu_0.55Sr_0.45MnO₃, including a ferromagnetic (in which the charge carriers concentrate due to a gain in the s-d exchange energy) and two antiferromagnetic phases (of the A and CE types). The volumes of these phases at low temperatures are evaluated. It is shown that the colossal magnetoresistance and the giant volume magnetostriction are related to the ferromagnetic phase formed as a result of the magnetic-field-induced transition of the CE-type antiferromagnetic phase to the ferromagnetic state.     

Charge transfer over localized states in a TlS single crystal

It is revealed that TlS single crystals exhibit a variable range hopping conduction along a normal to their natural layers at temperatures T ≤ 230 K in a dc electric field and a nonactivated hopping conduction at low temperatures in strong electric fields. Estimates are made for the density of states near the Fermi level (N _F = 2.8 × 10²⁰ eV^?1 cm^?3 and their energy spread (ΔW = 0.02 eV), the localization radius (a = 33 Å), the average jump distance in the region of activated (R _av(T) = 40 Å) and nonactivated (R _av(F) = 78 Å) hopping conduction, and also the drop in the charge carrier potential energy along the jump distance in an electric field F: eFR = 0.006 and 0.009 eV at F = 7.50 × 10³ and 1.25 × 10⁴ V/cm, respectively.     

Phasenumwandlung zweiter Art als kritische Erscheinung eines inneren Phasengleichgewichtes

It is demonstrated that the transition in a state with two internal phases is a second order phase transition. The term internal phases means phase-like regions inside the system which are not separated by boundaries in the sense of ordinary phase boundaries, and the dimensions and shape of which as well as their properties as such are object of an equilibrium. In a generalization (quasi phases) a long ranged correlation of alternating or periodical character is considered as a typical element of the low temperature state. Such states can be described thermodynamically with the help of a new pair of variablesQ-η. The transition intoQ-η-T is generally analogous to the critical point of ordinary phase transitions inP-V-T, andη ～(?t)^1/3 andC _p～(?t)^?2/3 with a small constant of proportionality are obtained (t=T-T _u). Using the Pippard-relations in the formV-V _γ=(dT _γ/dP) (S-S _γ) the low temperature behaviour of the entropy and density surface as a function ofP andT near the transition line can be completely described. E.g. the saturation magnetization of a ferromagnetic model is derived proportional to (?t)^1/3. Under the action of a magnetic field the transition will be of first order when the saturation magnetization is achieved, without the outer field being analogous toP orQ. Should only one internal phase differ from the high temperature state we obtain an edge point (x=0 analogous to theμ ₁?x-diagram of solutions) with finite jump inC _p andη～({t). A possible relationship to the BCS- model of the supraconductors is indicated.     

Distribution function of the number of particles in the condensate of an ideal Bose gas confined by a trap

The distribution function W₀(n₀) of the number n₀ of particles in the condensate of an ideal Bose gas confined by a trap is found. It is shown that at the temperature below the critical temperature T_c this function has a Gaussian shape and depends on the trap potential via two parameters only. The center of this function shifts to larger values of n₀ with decreasing temperature and its width tends to zero, which corresponds to the suppression of fluctuations. In the narrow vicinity of the critical temperature \(\left| {T - {T_c}} \right| \leqslant {T_c}/\sqrt N \), where N is the number of particles in the trap, the distribution function changes and at the temperature above the critical one it takes the usual form W₀(n₀) = [1 ? exp(μ)]exp(μn₀), where μ is the chemical potential in temperature units. In the limit N→∞, this change occurs at a jump.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

Gaussian free field in the background of correlated random clusters,formed by metallic nanoparticles

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T ? T _c . The fractal dimension of iso-potential lines (D _f ), the exponent of the distribution function of the gyration radius (τ _r ), and the loop lengths (τ _l ), and also the exponent of the loop Green function x _l change in terms of T ? T _c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D _f (T) ? D _f (T _c ) ~ 1/√ξ(T), in which ξ(T) is the spin correlation length in the Ising model.     

Peculiarities of magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Eu<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript>

Magnetic, elastic, magnetoelastic, transport, and magnetotransport properties of the Eu_0.55Sr_0.45MnO₃ ceramics have been studied. A break was detected in the temperature dependence of electrical resistivity ρ(T) near the temperature of the magnetic phase transformation (41 K), with the material remaining an insulator down to the lowest measurement temperature reached (ρ=10⁶ Ω cm at 4.2 K). In the interval 4.2≤T≤50 K, the isotherms of the magnetization, volume magnetostriction, and ρ were observed to undergo jumps at the critical field H_C1, which decreases with increasing T. For 50≤T≤120 K, the jumps in the above curves persist, but the pattern of the curves changes and H_C1 grows with increasing T. The magnetoresistance Δρ/ρ = (ρ _H ?ρ_H=0)/ρ _H is positive for H<H_C1 and passes through a maximum at 41 K, where Δρ/ρ = 6%. For H>H_C1, the magnetoresistance is negative, passes through a minimum near 41 K, and reaches a colossal value of 3×10⁵ % at H=45 kOe. The volume magnetostriction is negative and attains a giant value of 4.5×10^?4atH=45 kOe. The observed properties are assigned to the existence of three phases in Eu_0.55Sr_0.45MnO₃, namely, a ferromagnetic (FM) phase, in which carriers are concentrated because of the gain in s-d exchange energy, and two antiferromagnetic (AFM) phases of the A and CE types. Their fractional volumes at low temperatures were estimated to be as follows: ～3% of the sample volume is occupied by the FM phase; ～67%, by the CE-type AFM phase; and ～30%, by the A-type AFM phase.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

Free Energy as a Dynamical Invariant (or Can You Hear the Shape of a Potential?)

Classical lattice spin systems provide an important and illuminating family of models in statistical physics. An interaction Φ on a lattice L?? ^d determines a lattice spin system with potential A _Φ . The pressure P(A _Φ ) and free energy F _AΦ (β)=?(1/β)P(βA _Φ ) are fundamental characteristics of the system. However, even for the simplest lattice spin systems, the information about the potential that the free energy captures is subtle and poorly understood. We study whether, or to what extent, (microscopic) potentials are determined by their (macroscopic) free energy. In particular, we show that for a one-dimensional lattice spin system, the free energy of finite range interactions typically determines the potential, up to natural equivalence, and there is always at most a finite ambiguity; we exhibit exceptional potentials where uniqueness fails; and we establish deformation rigidity for the free energy. The proofs use a combination of thermodynamic formalism, algebraic geometry, and matrix algebra. In the language of dynamical systems, we study whether a Hölder continuous potential for a subshift of finite type is naturally determined by its periodic orbit invariants: orbit spectra (Birkhoff sums over periodic orbits with various types of labeling), beta function (essentially the free energy), or zeta function. These rigidity problems have striking analogies to fascinating questions in spectral geometry that Kac adroitly summarized with the question ``Can you hear the shape of a drum?''.     

Calculation of the binding energy of heavy nuclei with non-local two-body forces

A non-local, separable potential which matches the phase shifts up to 320 MeV and gives saturation for nuclear matter in the first order at a Fermi-momentum ofk _F =1.6 f^?1 with an energy per particle of ?8 MeV has been constructed byTabakin. We have employed this potential for calculations of finite nuclei using the Fermi-gas-model. The binding energy has been minimalized with respect to two parametersb andc (the surface-thickness and the radius of the nucleus). However the calculations show that an arbitrarily sharp surface is possible.     

Role of initial correlation in coarsening of a ferromagnet

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of theIsing model, employing the Glauber spin-flip mechanism, in space dimensionsd = 2 and3, on square and simplecubic lattices. Results for the persistence probability and the domain growth arediscussed for quenches to various temperatures (T _f ) below the criticalone (T _c ), from differentinitial temperatures T _i ≥T _c . In long timelimit, for T _i >T _c ,the persistence probability exhibits power-law decay with exponents θ ? 0.22 and? 0.18 in d = 2 and 3, respectively. For finite T _i , the early timebehavior is a different power-law whose life-time diverges and exponent decreases asT _i →T _c . The two steps areconnected via power-law as a function of domain length and the crossover to the secondstep occurs when this characteristic length exceeds the equilibrium correlation length atT =T _i . T _i =T _c is expected toprovide a new universality class for which we obtain θ ≡θ _c ? 0.035 ind = 2 and?0.105 in d = 3. The time dependenceof the average domain size ?, however, is observed to be rather insensitive tothe choice of T _i .